The Effect of Substratum Roughness on Osteoclast-like Cells In Vitro

Calcium phosphate powders were used to produce three groups of experimental substrata for the culture of primary rat bone marrow cells in conditions which permitted the survival and function of osteoclasts. Each of the three experimental groups were subdivided by differences in substratum surface roughness and following a culture period of 7 to 11 days, the culture units were stained for tartrate-resistant acid phosphatase activity. In all samples both small, sometimes mononuclear, and large multinucleate cells stained positive for tartrate-resistant acid phosphatase activity and the numbers and types of cells were quantified and statistically analyzed. Following histochemical staining the samples were dehydrated and gold coated for examination by scanning electron microscopy. Cells were found to create distinct resorption lacunae in most substrata, but not on the dense, high temperature sintered hydroxyapatite, and cells responsible for this activity were confirmed as exhibiting positive tartrate resistant acid phosphatase activity. Statistical analyses showed that both the total number of tartrate-resistant acid phosphatase positive cells and the number of multinucleate tartrate-resistant acid phosphatase positive cells was greater on the rougher than the smoother surfaces

Theory of high harmonic generation in relativistic laser interaction with overdense plasma

High harmonic generation due to the interaction of a short ultra relativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultra relativistic similarity theory we show that the high harmonic spectrum is universal, i.e. it does not depend on the interaction details. The spectrum includes the power law part $I_n\propto n^{-8/3}$ for $n<\sqrt{8\alpha}\gamma_{\max}^3$, followed by exponential decay. Here $\gamma_{\max}$ is the largest relativistic $\gamma$-factor of the plasma surface and $\alpha$ is the second derivative of the surface velocity at this moment. The high harmonic cutoff at $\propto \gamma_{\max}^3$ is parametrically larger than the $4 \gamma_{\max}^2$ predicted by the ``oscillating mirror'' model based on the Doppler effect. The cornerstone of our theory is the new physical phenomenon: spikes in the relativistic $\gamma$-factor of the plasma surface. These spikes define the high harmonic spectrum and lead to attosecond pulses in the reflected radiation.Comment: 12 pages, 9 figure

Influence of Crystal Structure on the Establishment of the Bone-Calcium Phosphate Interface In Vitro

An in vitro rat bone marrow cell system was used to examine the interfacial ultrastructure established between various calcium phosphates and mineralized tissue. The investigated calcium phosphates comprised hydroxyapatite (HA), fluorapatite (FA), tricalcium phosphate (TCP), tetracalcium phosphate (TECP) and magnesium whitlockite (MWL). Both scanning and transmission electron microscopy were used to examine the elaborated interface. The time in which a mineralized extracellular matrix was formed on the various materials differed from 2 weeks on HA, TCP and TECP, to 8 weeks on FA. It was only occasionally observed in some areas on MWL, which might have been due to aluminum impurities in the coating. With transmission electron microscopy, three distinct interfacial structures were observed. They differed in the presence or absence of a collagen free, 0. 7 to 0. 8 J.Lm wide, amorphous zone and a 20 to 60 nm thick electron dense layer , interposed between the material surface and the mineralized extracellular matrix. The electron dense layer was considered to be at least partially caused by protein adsorption , which would precede or concur with biological mineralization events , while the amorphous zone was regarded to represent partial degradation of the calcium phosphate surfaces. The results of this study show that plasma sprayed calcium phosphates will display different bone-bonding and biodegradation properties , depending on their chemical composition and crystal structures

Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander

In Vitro Bone Formation Associated with Apatite Coated Polylactide

Bone formation onto poly(L-lactide), which was plasma-spray coated with various quantities of hydroxyapatite (0%, 15%, 36% and 100% coverage), was investigated in an in vitro assay. Rat bone marrow cells were grown on the different coatings and the cellular response and elaborated extracellular matrix was examined at the light and electron microscopical level after 1, 2 , 4 and 8 weeks of culture. Proliferation of cells into multilayers was seen on the 0% , 36% and 100% , but not on the 15 % coatings. Coinciding with this was the sparse formation of extracellular matrix on the latter, and its abundant appearance on the former three coatings. Scanning and transmission electron microscopy revealed a mineralized extracellular matrix on the 100% and 36% coatings after 2 and 4 weeks , respectively, and on the 15 % coating after 8 weeks. Mineralization was not observed on uncoated poly(L-lactide). At the interface between hydroxyapatite and the mineralized extracellular matrix, one or more electron dense layers were frequently observed , which showed morphological similarities with structures between these two entities in vivo. The results of this in vitro study show that, in the model used, hydroxyapatite is required to obtain the elaboration of mineralized extracellular matrix on poly(L-lactide)

Probability distributions for quantum stress tensors in four dimensions

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional spacetime. Specifically, there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. We are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bounds, the asymptotic forms for large positive argument, and possible fits to the intermediate region. The first 65 moments are used for these purposes. All of our results are subject to the caveat that these distributions are not uniquely determined by the moments. However, we also give bounds on the cumulative distribution function that are valid for any distribution fitting these moments.We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.Comment: 26 pages, 2 figure

Energy-Filtering Transmission Electron Microscopy of Biological Specimens

By energy-filtering transmission electron microscopy (EFTEM) electrons can be separated by their energy losses. An electron-energy filter, added to the microscope column allows the measurement of the energy distribution of transmitted electrons that have lost energy (\u3c 2,000 eV, with an energy resolution of ~ 1 eV). These filtered electrons, recorded either as a spectrum or as an image, are composed of two parts superimposed on top of each other: (a) the unspecific energy-loss population (= the continuum) and (b) the specific element-related energy-loss population (= the edges). At the edges, electron data in spectra and images are mathematically processed, to obtain the desired element-related net-intensity values or images. These data are related to the total transmitted electron intensity, from the zero-and low-loss spectral region giving the relative spectral-or image intensity ratios (SR*x, IR*x), which can be related to the element concentration. The acquisition of the zero-loss and low-loss data is hampered by the restricted dynamic range of the TV camera. By improvements through the introduction of calibrated attenuation filters in the optical path to the TV-camera, more reliable values for SR*x and IR*x can be acquired. By addition of Bio-standards adjacent to the tissue, a known and unknown concentration of the element present in the same ultrathin section and the bias in the concentration estimation, can be obtained. Some practical examples are given for the estimation of the iron concentration in siderosomes, boron in melanosomes and calcium in calcium oxalate monohydrate crystals